We may also consider stabilization based on patches or macro elements, which is the form that was presented with the introduction of the ghost penalty in [1]} and, for a certain choice of patches, is also considered in [2]}. With this form of stabilization, each cut element is associated with a patch of neighboring elements that contains at least one element in the interior. We may then penalize the difference between the finite element function and a global polynomial on the patch. More precisely, let \(M_T\)  be a patch of elements containing \(T\) , then we can define
\(\begin{aligned}s_{h,0}^{\mathrm {patch}}(w_h,v_h) & = \sum _{T\in \mathcal {T}_h^{\textrm {cut}}} \tau _0 h^{-2}( w_h - P_p w_h, v_h - P_p v_h )_{M_T} \\s_{h,1}^{\mathrm {patch}}(w_h,v_h) & = \sum _{T\in \mathcal {T}_h^{\textrm {cut}}} \tau _1 (\nabla (w_h - P_p w_h), \nabla (v_h - P_p v_h) )_{M_T}\end{aligned}\) 
